Geometric sequence

We can modify the dots and to see a geometric sequence representation.

The gray dot allow us to modify the ordinate axe scale.

The dots in the Y-axe forms a geometric sequence and the dots in the X-axe forms an aritmetic trivial sequence.

When the ratio r is grater than 1 we have a increasing sequence.

If the ratio is less than 1 the sequence is decreasing and the general term tends to 0.

If we see the sequence as a function, its domain is the natural numbers. We can easily extends this domain to be the integers. We want to extends this function to the rationals and to the reals numbers.

LINKS

	Sum of a geometric series of ratio 1/4 One intuitive example of how to sum a geometric series. A geometric series of ratio less than 1 is convergent.
	Sum of a geometric series of ratio 1/2 The geometric series of ratio 1/2 is convergent. We can represent this series using a rectangle and cut it in half successively. Here we use a rectangle such us all rectangles are similar.
	Geometric sequence Geometric sequences graphic representations